The problem asks about the relationship between the graph of $f(x)$ and $g(x) = f(x) - 1$.

Solution:

• When a constant is subtracted from the function $f(x)$, like $f(x) - 1$, this corresponds to a vertical shift downward by 1 unit.
  • Subtracting a constant affects the y-values of the graph, moving the entire graph downward without changing the x-values.

Thus, the correct option is:

"The graph of $g(x)$ is the graph of $f(x)$ translated 1 unit down."

Would you like further explanation or have any other questions?

Here are five related questions you might find helpful:

1. What happens when you add a constant to a function, like $f(x) + 2$?
2. How does translating a graph horizontally differ from vertical translations?
3. What is the effect of multiplying a function by a negative constant?
4. How can you identify transformations (shifts, stretches) just by looking at a function?
5. Can you give an example of a horizontal translation, and how it affects the graph?

Tip: A vertical translation changes only the y-values, while a horizontal shift affects the x-values.